In my pocket dictionary I find for affinity: tendency, (spiritual) relation. I would say: Kulturverwandschaft. (Hello, Toadfrog: the candidate got 89 points.)
In German the culture is often named with an added -philie (from the Greek stem *phil = friend, love &c. as in Philadelphia = brotherly love).
So we have Hellenophilie = love to Greece, Greeks or Greek culture, Turkophilie = to the Turks, Anglophilie = the the English speaking (incl. Welsh, Scots, Irish, Americans &c.) and so on.

Wilfried